Angular Deficit Research Articles

Dynamics of spin-0 (particles-antiparticles) in Bonnor-Melvin cosmological space-time using the Generalized Feshbach-Villars transformation

In this paper, we employ the Generalized Feshbach-Villars transformation (GFVT) to investigate the relativistic quantum dynamics of spin-0 scalar particles within the backdrop of a magnetic universe characterized by the Bonnor-Melvin cosmological space-time, which exhibits a geometrical topology resulting in an angular deficit. We derive the radial equation of the Klein-Gordon equation using this FV representation and obtain analytical solutions utilizing special functions. Our analysis demonstrates that various parameters associated with the space-time geometry exert significant influence on the eigenvalue solutions within this novel representation.

Terrestrial planet formation from a ring: Long-term simulations accounting for the giant planet instability

The process leading to the formation of the terrestrial planet remains elusive. In a previous publication, we have shown that, if the first generation of planetesimals forms in a ring at ∼1 AU and the gas disk's density peaks at the ring location, planetary embryos of a few martian masses can grow and remain in the ring. In this work, we extend our simulations beyond the gas-disk stage, covering ∼200 Myr and accounting for the phase of giant planet instability, assumed to happen at different times. About half of the simulations form a pair of Venus and Earth analogues and, independently, about 10% form a Mars analogue. We find that the timing of the giant planet instability affects statistically the terrestrial system's excitation state and the timing of the last giant impacts. Hence a late instability (∼60 to 100 Myr after the Solar system's birth) is more consistent with a late Moon-formation time, as suggested by radioactive chronometers. However, the late veneer mass (LVM: mass accreted after the last giant impact) of Earth-sized planets suffering a giant impact after 80 My is usually an order of magnitude lower than the value inferred from geochemistry. In addition, the final angular momentum deficit (AMD) of the terrestrial planets tends to be too high. We tested the effect on the final AMD of the generation of debris during collisions and found that it is too small to change these conclusions. We argue that the best-case scenario is that the Moon-forming event occurred between 50 and 80 My, possibly just following the giant planet instability.

Kepler Multitransiting System Physical Properties and Impact Parameter Variations

We fit a dynamical model to Kepler systems that contain four or more transiting planets using the analytic method AnalyticLC and obtain physical and orbital parameters for 101 planets in 23 systems, of which 95 are of mass significance better than 3σ, and 46 are without previously reported mass constraints or upper limits. In addition, we compile a list of 71 Kepler objects of interest that display significant transit impact parameter variations (TbVs), complementing our previously published work on two- and three-transiting-planet systems. Together, these works include the detection of significant TbV signals of 130 planets, which is, to our knowledge, the largest catalog of this type to date. The results indicate that the typical detectable TbV rate in the Kepler population is of order 10−2 yr−1 and that rapid TbV rates (≳0.05 yr−1) are observed only in systems that contain a transiting planet with an orbital period less than ∼20 days. The observed TbV rates are only weakly correlated with orbital period within Kepler’s ≲100-day-period planets. If this extends to longer periods, it implies a limit on the utility of the transit technique for long-period planets. The TbVs we find may not be detectable in direct impact parameter measurements, but rather are inferred from the full dynamics of the system, encoded in all types of transit variations. Finally, we find evidence that the mutual inclination distribution is qualitatively consistent with the previously suggested angular momentum deficit model using an independent approach.

Hot Jupiter formation in dense star clusters

ABSTRACT Hot Jupiters (HJ) are defined as Jupiter-mass exoplanets orbiting around their host star with an orbital period < 10 d. It is assumed that HJ do not form in-situ but ex-situ. Recent discoveries show that star clusters contribute to the formation of HJ. We present direct N-body simulations of planetary systems in star clusters and analyse the formation of HJ in them. We combine two direct N-body codes: nbody6++gpu for the dynamics of dense star clusters with 32 000 and 64 000 stellar members and lonelyplanets used to follow 200 identical planetary systems around solar mass stars in those star clusters. We use different sets with three, four, or five planets and with the innermost planet at a semimajor axis of 5 or 1 au and follow them for 100 Myr in our simulations. The results indicate that HJs are generated with high efficiency in dense star clusters if the innermost planet is already close to the host star at a semimajor axis of 1 au. If the innermost planet is initially beyond a semimajor axis of 5 au, the probability of a potential HJ ranges between 1.5 and 4.5 per cent. Very dense stellar neighbourhoods tend to eject planets rather than forming HJs. A correlation between HJ formation and angular momentum deficit is not witnessed. Young HJs (tage < 100 Myr) have only been found, in our simulations, in planetary systems with the innermost planet at a semimajor axis of 1 au.

The GAPS programme at TNG

Context. Observational data from space- and ground-based campaigns have revealed that the 10-30 Ma old V1298Tau star hosts a compact and massive system of four planets. Mass estimates are available for the two outer giant planets and point to unexpectedly high densities for their young ages. Aims. We investigate the formation of these two outermost giant planets, V1298 Tau b and e, and the present dynamical state of V1298 Tau’s global architecture in order to shed light on the history of this young and peculiar extrasolar system. Methods. We performed detailed N-body simulations to explore the link between the densities of V1298 Tau b and e and their migration and accretion of planetesimals within the native circumstellar disk. We combined N-body simulations and the normalized angular momentum deficit (NAMD) analysis of the architecture to characterize V1298 Tau’s dynamical state and connect it to the formation history of the system. We searched for outer planetary companions to constrain V1298 Tau’s planetary architecture and the extension of its primordial circumstellar disk. Results. The high densities of V1298 Tau b and e suggest they formed at quite a distance from their host star, likely beyond the CO2 snowline. The higher nominal density of V1298 Tau e suggests it formed farther out than V1298 Tau b. The current architecture of V1298 Tau is not characterized by resonant chains. Planet-planet scattering with an outer giant planet is the most likely cause for the lack of a resonant chain between V1298 Tau’s planets, but currently our search for outer companions using SPHERE and Gaia observations can exclude only the presence of planets more massive than 2 MJ. Conclusions. The most plausible scenario for V1298 Tau’s formation is that the system formed by convergent migration and resonant trapping of planets born in a compact and plausibly massive disk. In the wake of their migration, V1298 Tau b and e would have left a dynamically excited protoplanetary disk, naturally creating the conditions for the later breaking of the resonant chain by planet-planet scattering.

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. Perfect fluids

In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D 104, 064040 (2021); J. Math. Phys. 64, 022501 (2023); J. Math. Phys. 64, 032501 (2023); J. Math. Phys. 64, 042501 (2023); and J. Math. Phys. 64, 052502 (2023)]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed.

Chaos in multiplanetary extrasolar systems

ABSTRACT Here, we present an initial look at the dynamics and stability of 178 multiplanetary systems that are already confirmed and listed in the NASA Exoplanet Archive. To distinguish between the chaotic and regular nature of a system, the value of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) indicator for each system was determined. Almost three-quarters of them could be labelled as long-term stable. Only 45 studied systems show chaotic behaviour. We consequently investigated the effects of the number of planets and their parameters on the system stability. A comparison of results obtained using the MEGNO indicator and machine-learning algorithm SPOCK (Stability of Planetary Orbital Configuration Klassifier) suggests that the SPOCK could be used as an effective tool for reviewing the stability of multiplanetary systems. A similar study was already published by Laskar and Petit. We compared their analysis based on the AMD (Angular Momentum Deficit) criterion with our results. The possible discrepancies are discussed.

Instability from high-order resonant chains in wide-separation massive planet systems

ABSTRACT Diversity in the properties of exoplanetary systems arises, in part, from dynamical evolution that occurs after planet formation. We use numerical integrations to explore the relative role of secular and resonant dynamics in the long-term evolution of model planetary systems, made up of three equal mass giant planets on initially eccentric orbits. The range of separations studied is dominated by secular processes, but intersects chains of high-order mean-motion resonances. Over time-scales of 108 orbits, the secular evolution of the simulated systems is predominantly regular. High-order resonant chains, however, can be a significant source of angular momentum deficit (AMD), leading to instability. Using a time series analysis based on a Hilbert transform, we associate instability with broad islands of chaotic evolution. Previous work has suggested that first-order resonances could modify the AMD of nominally secular systems and facilitate secular chaos. We find that higher order resonances, when present in chains, can have similar impacts.

Noninertial effects on a composite system

In this paper, we investigate the relativistic dynamics of a fermion–antifermion pair holding through Dirac oscillator interaction in the rotating frame of [Formula: see text]-dimensional topological defect-generated geometric background. We obtain an exact energy spectrum for the system in question by solving the corresponding form of a fully covariant two-body Dirac equation. This energy spectrum depends on the angular velocity [Formula: see text] of uniformly rotating frame and angular deficit [Formula: see text] in the geometric background. Our results show that the effects of [Formula: see text] on each energy level of the system are not same and the [Formula: see text] impacts on the strength of interaction between the particles. Furthermore, we observe that it seems to be possible to actively tune the dynamics of such a fermion–antifermion system, in principle.

A Criterion for the Onset of Chaos in Compact, Eccentric Multiplanet Systems

Abstract We derive a semianalytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of chaos is determined by the overlap of two-body mean motion resonances (MMRs), like it is in two-planet systems; and (ii) secular evolution causes the MMR widths to expand and contract adiabatically, so that the chaotic boundary is established where MMRs overlap at their greatest width. For closely spaced two-planet systems, a near symmetry strongly suppresses this secular modulation, explaining why the chaotic boundaries for two-planet systems are qualitatively different from cases with more than two planets. We use these results to derive an improved angular momentum deficit (AMD) stability criterion, i.e., the critical system AMD below which stability should be guaranteed. This introduces an additional factor to the expression from Laskar and Petit that is exponential in the interplanetary separations, which corrects the AMD threshold toward lower eccentricities by a factor of several for tightly packed configurations. We make routines for evaluating the chaotic boundary available to the community through the open-source SPOCK package.

Can a jumping-Jupiter trigger the Moon’s formation impact?

ABSTRACT We investigate the possibility that the Moon’s formation impact was triggered by an early dynamical instability of the giant planets. We consider the well-studied ‘jumping Jupiter’ hypothesis for the Solar system’s instability, where Jupiter and Saturn’s semimajor axes evolve in step-wise manner from their primordially compact architecture to their present locations. Moreover, we test multiple different configurations for the primordial system of terrestrial planets and the Moon-forming projectile, with particular focus on the almost equal masses impact. We find that the instability/migration of the giant planets excites the orbits of the terrestrial planets through dynamical perturbations, thus allowing collisions between them. About 10 per cent of the simulations lead to a collision with the proto-Earth which resulted in a final configuration of the terrestrial system that reproduces, to some extent, its present architecture. Most of these collisions occur in the hit-and-run domain, but about 15 per cent occur in the partial accretion regime, with the right conditions for a Moon-forming impact. In most of the simulations, there is a delay of more than ∼20 My between the time of the instability and the Moon-forming impact. This supports the occurrence of an early instability (<10 My after dissipation of the gas in the protoplanetary disc), compatible with the time of the Moon-forming impact (30–60 My) inferred from cosmochemical constraints. In general, the final states of the inner Solar system in our simulations show an excess of Angular Momentum Deficit, mostly attributed to the overexcitation of Mercury’s eccentricity and inclination.

Dynamics of a composite system in a point source-induced space–time

We investigate the dynamics of a composite system ([Formula: see text]) consisting of an interacting fermion–antifermion pair in the three-dimensional space–time background generated by a static point source. By considering the interaction between the particles as Dirac oscillator coupling, we analyze the effects of space–time topology on the energy of such a [Formula: see text]. To achieve this, we solve the corresponding form of a two-body Dirac equation (fully-covariant) by assuming the center-of-mass of the particles is at rest and locates at the origin of the spatial geometry. Under this assumption, we arrive at a nonperturbative energy spectrum for the system in question. This spectrum includes spin coupling and depends on the angular deficit parameter [Formula: see text] of the geometric background. This provides a suitable basis to determine the effects of the geometric background on the energy of the [Formula: see text] under consideration. Our results show that such a [Formula: see text] behaves like a single quantum oscillator. Then, we analyze the alterations in the energy levels and discuss the limits of the obtained results. We show that the effects of the geometric background on each energy level are not same and there can be degeneracy in the energy levels for small values of the [Formula: see text].

Effects of Rotating Frame on a Vector Boson Oscillator

We analyze the effects of the spacetime topology and angular velocity of rotating frame on the dynamics of a relativistic vector boson oscillator (VBO). To determine these effects on the energy of the VBO we solve the corresponding vector boson equation in the rotating frame of 2+1 dimensional cosmic string-induced spacetime background. We obtain an exact energy spectrum, which depends on the angular velocity of the rotating frame and angular deficit parameter of the background. We show that the effects of angular deficit parameter on each energy level of the VBO cannot be same and the angular velocity of the rotating frame couples with the spin of the VBO. Furthermore, we have obtained that the angular velocity of rotating frame breaks the symmetry of the positive-negative energy states.

Non-singular vortices with positive mass in 2+1-dimensional Einstein gravity with AdS3 and Minkowski background

In previous work, black hole vortex solutions in Einstein gravity with AdS3 background were found where the scalar matter profile had a singularity at the origin r = 0. In this paper, we find numerically static vortex solutions where the scalar and gauge fields have a non-singular profile under Einstein gravity in an AdS3 background. Vortices with different winding numbers n, VEV v and cosmological constant Λ are obtained. These vortices have positive mass and are not BTZ black holes as they have no event horizon. The mass is determined in two ways: by subtracting the numerical values of two separate asymptotic metrics and via an integral that is purely over the matter fields. The mass of the vortex increases as the cosmological constant becomes more negative and this coincides with the core of the vortex becoming smaller (compressed). We then consider the vortex with gravity in asymptotically flat spacetime for different values of the coupling α = 1/(16πG). At the origin, the spacetime has its highest curvature and there is no singularity. It transitions to an asymptotic conical spacetime with angular deficit that increases significantly as α decreases. For comparison, we also consider the vortex without gravity in flat spacetime. For this case, one cannot obtain the mass by the first method (subtracting two metrics) but remarkably, via a limiting procedure, one can obtain an integral mass formula. In the absence of gauge fields, there is a well-known logarithmic divergence in the energy of the vortex. With gravity, we present this divergence in a new light. We show that the metric acquires a logarithmic term which is the 2 + 1 dimensional realization of the Newtonian gravitational potential when General Relativity is supplemented with a scalar field. This opens up novel possibilities which we discuss in the conclusion.

Architectures of Exoplanetary Systems. III. Eccentricity and Mutual Inclination Distributions of AMD-stable Planetary Systems

AbstractThe angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criterion to constrain the orbital architectures for exoplanetary systems. Previously, He et al. showed through forward modeling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit can also match the observed Kepler population. We show that distributing a planetary system’s maximum AMD among its planets results in a multiplicity-dependent distribution of eccentricities and mutual inclinations. Systems with intrinsically more planets have lower median eccentricities and mutual inclinations, and this trend is well described by power-law functions of the intrinsic planet multiplicity (n):and, whereandare the medians of the eccentricity and inclination distributions. We also find that intrinsic single planets have higher eccentricities (σe,1 ∼ 0.25) than multiplanet systems and that the trends with multiplicity appear in the observed distributions of period-normalized transit duration ratios. We show that the observed preferences for planet-size orderings and uniform spacings are more extreme than what can be produced by the detection biases of the Kepler mission alone. Finally, we find that for systems with detected transiting planets between 5 and 10 days, there is another planet with a greater radial velocity signal ≃53% of the time.

An interacting fermion-antifermion pair in the spacetime background generated by static cosmic string

We consider a general relativistic fermion antifermion pair that they interact via an attractive Coulomb type interparticle interaction potential in the 2+1 dimensional spacetime background spanned by cosmic string. By performing an exact solution of the corresponding fully-covariant two body Dirac Coulomb type equation we obtain an energy spectrum that depends on angular deficit parameter of the static cosmic string spacetime background for such a composite system. We arrive that the influence of cosmic string spacetime topology on the binding energy of Positronium-like atoms can be seen in all order of the coupling strength constant, even in the well-known non-relativistic binding energy term (∝αc2). We obtain that the angular deficit of the static cosmic string spacetime background causes a screening effect. For a predicted value of angular deficit parameter, α∼1−10−6, we apply the obtained result to an ortho-positronium, which is an unstable atom formed by an electron and its antimatter counterpart a positron, and then we determine the shift in the ground state binding energy level as 27,2μeV. We also arrive that, in principle, the shift in ground state binding energy of ortho-positronium can be measured even for α∼1−10−11 value with current techniques in use today. Moreover, this also gives us an opportunity to determine the altered total annihilation energy transmitted by the annihilation photons. The yields also impose that the total lifetime of an ortho-positronium can be changed by the topological feature of static cosmic string spacetime background. In principle, we show that an ortho-positronium system has a potential to prove the existence of such a spacetime background.

Parametric instability in a free-evolving warped protoplanetary disc

ABSTRACT Warped accretion discs of low viscosity are prone to hydrodynamic instability due to parametric resonance of inertial waves as confirmed by local simulations. Global simulations of warped discs, using either smoothed particle hydrodynamics or grid-based codes, are ubiquitous but no such instability has been seen. Here, we utilize a hybrid Godunov-type Lagrangian method to study parametric instability in global simulations of warped Keplerian discs at unprecedentedly high resolution (up to 120 million particles). In the global simulations, the propagation of the warp is well described by the linear bending-wave equations before the instability sets in. The ensuing turbulence, captured for the first time in a global simulation, damps relative orbital inclinations and leads to a decrease in the angular momentum deficit. As a result, the warp undergoes significant damping within one bending-wave crossing time. Observed protoplanetary disc warps are likely maintained by companions or aftermath of disc breaking.

Hybrid Metric-Palatini Gravity: Regular Stringlike Configurations

We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field ϕ and a self-interaction potential V(ϕ). The ϕ field can be canonical or phantom, and, accordingly, the theory splits into canonical and phantom sectors. We seek solitonic (stringlike) vacuum solutions of HMPG, that is, completely regular solutions with Minkowski metric far from the symmetry axis, with a possible angular deficit. A transition of the theory to the Einstein conformal frame is used as a tool, and many of the results apply to the general Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories as well as f(R) theories of gravity. One of these results is a one-to-one correspondence between stringlike solutions in the Einstein and Jordan frames if the conformal factor that connects them is everywhere regular. An algorithm for the construction of stringlike solutions in HMPG and scalar-tensor theories is suggested, and some examples of such solutions are obtained and discussed.

The GAPS programme at TNG

Context. With the growth of comparative exoplanetology, it is becoming increasingly clear that investigating the relationships between inner and outer planets plays a key role in discriminating between competing formation and evolution models. To do so, it is important to probe the inner region of systems that host long-period giants in search of undetected lower-mass planetary companions. Aims. In this work, we present our results on the K-dwarf star BD-11 4672, which is already known to host a long-period giant planet, as the first output of a subsample of the GAPS programme specifically aimed at assessing the impact of inefficient migration of planets formed beyond the snowline by searching for Neptune-mass and super-Earth planetary companions of known longer-period giants. Methods. We used the high-precision HARPS-N observations of BD-11 4672 in conjunction with time series taken from the literature in order to search for additional inner planetary signals to be fitted using differential evolution Markov chain Monte Carlo. The long-term stability of the new orbital solutions was tested with N-body dynamical simulations. Results. We report the detection of BD-11 4672 c, a new Neptune-mass planet with an orbital period of 74.20−0.08+0.06 d, eccentricity of 0.40−0.15+0.13, semimajor axis of 0.30 ± 0.01 au, and minimum mass 15.37−2.81+2.97 M⊕, orbiting slightly outside the inner edge of the optimistic circumstellar habitable zone. In order to assess its impact on the dynamical stability of the habitable zone, we computed the angular momentum deficit of the system, showing that planet c has a severe negative impact on the stability of possible additional lower-mass temperate planets. The BD-11 4672 system is notable for its architecture, hosting both a long-period giant planet and an inner lower-mass planet, the latter being one of the most eccentric Neptune-mass planets known at similar periods.

Dynamical Instabilities in Systems of Multiple Short-period Planets Are Likely Driven by Secular Chaos: A Case Study of Kepler-102

We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ~ 20% of the cases on a wide range of timescales (up to 5×109 orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multi-planet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet-planet collisions in ~ 80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳ 0.1M ⊕, hence a bulk density exceeding about half Earth's, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system's AMD evolution with a "spectral fraction" calculated from the power spectrum of short integrations (~ 5 × 106 orbits). We find that small spectral fractions (≲ 0.01) are strongly associated with dynamical stability on long timescales (5 × 109 orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many non-resonant multi-planet systems, and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long term (in)stability of multi-planet systems from short simulations.